I am not a cruise expert AT ALL -- but we went on an Alaskan Cruise on the Coral Princess two summers ago. It's not the same ship, but it looks like it's kind of a similar size.
The Coral Princess had a public balcony across the back of our deck, but we were the first cabin forward of the public balcony. (We had a separate private balcony to the side.) My sister's family was a few cabins farther forward from us. I believe some other decks had cabins with aft-facing balconies.
Regarding vibration -- we could feel some vibrations while we were laying quietly on the bed. It just kind of shook the bed gently. When we cruised on the Disney Dream, we were right above the movie theater and they played The Avengers on repeat. I think we felt more vibrations from the sound effects from that. Both were "noticeable" if you were laying quietly... but not none of them really disturbed us (slept fine, etc.)
We really enjoyed hanging out on the public aft-facing balcony. It was much larger than our side-facing ones so my sister's family and mine could all hang out there together (something we couldn't have done in anyone's cabins). Although the cabins with the aft-facing balconies probably wouldn't have been nearly as large as the public one... they did look like they were considerably deeper than the side-facing balconies. On our ship, the aft-facing balconies had chaise lounge chairs, while the side-facing had regular deck chairs (and those were a tight fit.) Based on what I experienced on the Coral Princess, I would consider booking an aft-facing cabin if it had a large balcony.
Similar to sonnyjane's point, though -- on certain decks there was a set-back, so those balconies were not 'covered' by the balcony above them. (This meant not only did rain fall on those balconies, the higher decks could look down onto them.) On our ship, this was true for certain decks on both the sides and the back... but not all decks. But that's not something I "noticed" when looking at the deck plans. However, if we cruise again, I will definitely check more closely. (Our deck was covered, so we lucked out there.)